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1 Glassware Calibration Guidelines Laura B. Secor and Dwight R. Stoll, 02/0/202 Adapted from National Bureau of Standards Document The purpose of calibrating glassware is to determine the volume of liquid that the glassware actually holds, as opposed to the advertised or stated volume. The volume of water contained in glassware is derived from the mass, using density as a conversion factor. The indicated mass of the water (M I) is easy to calculate, by subtracting the weight of an empty dry flask (M EF) from the weight of the full flask (M FF), as measured using an analytical balance. M I = M FF M EF Eq. However, depending on the level of accuracy desired, a series of adjustments should be made to correct this value. The true mass of the water and the expansion of glass due to temperature can be accounted for as follows. Adjustment # - Buoyancy The buoyancy adjustment corrects the mass indicated by the balance in cases where the object being weighed does not have the same density as the material used to calibrate the balance. Balances measure weight through comparison to a calibration weight, typically a metal. The apparent mass of both the water and the calibration weight are affected by the air in which they re sitting. The air produces a buoyancy force counteracting the downward force applied by both the balance weights and the unknown water mass. An electronic balance works by comparison of these two forces. M W ρ A ρ W = M I ρ A ρ B Eq. 2 Here, M w refers to the corrected mass of water, M I is the mass as indicated by the balance, ρ is the typical symbol for density, B represents the calibration weights, and A stands for air. Typical analytical balances use counterweights with a density of 7.78 g/cm 3. Eq 2 rearranges to yield: ρ W M W = M I ρ A Eq. 3 ρ B ρ W ρ A To obtain the volume of water, divide the mass M W by the density of water for the temperature at which the measurements were made ρ W: V T = M I ρ A Eq. 4 This volume, V T, is the volume dispensed or contained by the piece of glassware, for the temperature at which the measurements were made. A final correction is required to account for expansion or contraction of the glass with temperature if a comparison of the volume of the device to the volume specified for 20 C is desired.

2 The density of water and air can often be found in tables if the temperature and pressure are known. If necessary, the following equations, where T is the temperature in C and B is the pressure in mm Hg, can be used to determine density. ρ A = B 40( T ) 000(T+273.6) Eq. 5 ρ W = (T )2 T T ( ) Eq. 6 Note that these equations yield densities with units of g/cm 3. When weighing an analyte other than water, a similar adjustment can be made, replacing ρ W with the density of the new material. Adjustment #2 - Glass Expansion/Contraction The above calculations result in the volume contained in the flask at the test temperature. Standard glass calibration yields the volume contained at 20 C. The expansion of the glassware should also be accounted for when highly accurate results are needed. This adjustment, K, is material dependent, calculated using K = - α(t-20) Eq. 7 where α is the temperature coefficient of cubical expansion (because the glass expands in three dimensions) and T is the test temperature in C. The majority of laboratory glassware is borosilicate, for which α = / C. Note that a larger α value or a temperature that differs greatly from 20 C will result in a larger K value. By accounting for glass expansion, the volume at 20 C (V 20) can be calculated. V 20 = M I ρ A [ α(t 20)] Eq. 8 The slightly condensed version isolates the contribution of each adjustment. V 20 = M I ρ A [K] Eq. 9

3 Sample Glassware Calibration Problem Note: for these problems it is useful to carry through more significant digits than is needed in the final answer. After carefully cleaning and drying a 00 ml volumetric flask, you measure its weight to be g. You fill the flask with water until the bottom of the meniscus is even with the full line, at which point the weight is 67.6 g. Two more replicates yield full flask weights of g and 67.8 g. Before moving on, you dutifully measure the temperature of the water to be 24.6 C and the barometric pressure to be 750 mmhg.. What is the indicated weight of the water (M I) in each of the three trials? Based on the conversion g water = ml water, what would you calculate the volume of your flask to be without any adjustments? What is the average of these measurements? 2. The density of the built-in weights in your analytical balance is 7.78 g/cm 3 ; density tables for air and water are attached. What is the value of the buoyancy adjustment for this set of measuremnts, ρ A? 3. You re using borosilicate glass, for which the temperature coefficient of cubical expansion (α) is / C. What is the glass expansion adjustment, K? 4. Taking into account all of these adjustments, what volume does this flask hold at 20 C in each of the three trials? What is the average? 5. What is the precision (relative standard deviation) of these measurements?

4 6. Using the average, unadjusted volume found in Problem, determine what you would find the final volume to be in each case if you ignored one of the adjustments? (i.e. ignore the buoyancy correction and incorporate only Q and K) 7. What are the absolute and relative errors associated with each of these measurements? 8. Which adjustment has the greatest effect? The least effect? 9. What adjustments might you feel safe ignoring? Justify your answer and mention circumstances in which you would not ignore the adjustment(s).

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